Arvind's Roar Profile

I tried looking for data sources with historical weather to check if the conditions at the time of toss were favorable for bowling or not. I couldn’t find any way to get historical weather beyond the last few years.

That would have allowed me to further fine tune the analysis along the dimension you allude to. Unfortunately I couldn’t make progress.

Jeff, your read is right. Theres matter of skill that can still influence a decision despite starting off with a disadvantage from batting second after losing a toss. The bat first advantage for toss winning captains has accrued steadily as seen in the charts but only accounts for 10 pct (loosely speaking) for wins.

Paul, you are right to an extent. Theres more to come on this analyses, but this merely shows that the field first decision has had a far weaker advantages – its a trickier decision because you have to weigh the short term advantage of some condition with the longer term diadvantage of having to bat fourth. I hope to share some of that analysis soon.

“Conditions could scarcely have been more difficult for batting – poor light against a hooping ball on a pitch offering extravagant seam movement.”

Likely that this was discernible at the time of the toss that England won. Ronan, please consider giving the below a read.

A better alternative to cricket’s coin toss

Warner's ugly but crucial Ashes innings

Thanks for explaining. I see your argument more clearly now – they bear resemblance those made by purist friends of min. Here are somethings to consider.

Decision making and forecasting is an integral part of cricket. “Whats a par score for this wicket” is a question that is routinely asked and almost always answered, by captains, cricketers and media presenters at the scheduled toss of an ODI. Anecdotally, as seen from comments during the recent world cup, teams seem to manage the first innings based on forecast from management and batsmen on the pitch. Another example, “Is the pitch going to turn later on and should we have an additional spinner therefore. ”

Second, in case you are overestimating (I am not saying you are) the difficulty of forecasting the value of conditions, consider how much progress has been made in cricket par score forecasting and win prediction while the ODI is underway. Or the phenomenal progress by Sabermetrics in baseball. It is simply a matter of time, and a few committed data analysts and fans, before we have a measurable and more reliable estimate of the value of a set of conditions that are available to public (at currently the toss time) and which captains can base their own tweaks on.

Thanks Jeff. I appreciate your thoughtful comments.

How would you propose to deal with one-offs such as league stage world cup games or elimination games.

Also, just a quick note on the odds. In a 3 match series, theres a 25 pct chance of one of the two teams winning the toss three times in a row. So if the two teams are evenly matched on other counts, this may have a material impact on the series.

Also, its unclear to me if the additional selection choice for the loser of the toss can materially affect the selection or is compensation enough. (Even in my proposal we don’t know if the runs are compensation enough – but it is constructed to guarantee no captain can be unhappy with the decision of who gets to bat first so long as he or she bids what they deem to be fair. Over time data analyses will get more precise on what’s the fair compensation for a given set of conditions.)

Thanks for your input.

Thank you Paul for your comments. I appreciate the time and vigor involved.

For (1) and (2), other factors such as tv audience, determine starting times. Unlikely that things will change. Furthermore, the material change in condition could arise just a few hours before start, such as dampness or predicted rain for later, that may affect only one of the sides. The issue is that the winner of the coin toss enjoys the rub of the favorable condition and that seems to show up in increasing winning odds – as seen in the study I linked to.

Let me address (4) first and then, (3)/(5). It is hard to know on a limited data set if the toss had any bearing on the data – no individual can claim to have keen insight on the counterfactual. However, consider the implications of an argument that “factor X did’nt have an impact on the result so its fine” – it would imply that giving Usain Bolt a 3 meter head start at the olympics is fine because the others would anyway lose to him; and it would also imply that it is fine for every other competitor, at least in Beijing 2008, to be given a 3m head start because Bolt would have won anyway. Another implication – Any perceived Russian tampering may not have affected the 2016 election, so it is fine for elections to allow external influence. So, I am not sure I agree with the structure of your argument.

Re(3) and (5), if there’s any perceived advantage to batting first or to avoid batting last in a test, the captain can bid a certain number of runs to bat first. If a captain perceives no such advantage he can simply bid 0. These perceived advantages are based on assessments a-priori and not post the event – your examples are post the event. If those perceived advantages don’t materialize in the game, either due to poor execution or other factors including mis-judgement about the conditions, theres little that can be done about them. My proposal only attempts to mitigate any known biases in conditions by offsetting with runs that the captains decide among’st themselves.

One of the upcoming Ashes tests is in Headingley where there seems to be some advantages to winning the toss. See: https://www.espncricinfo.com/story/_/id/22863861/win-toss-win-match.

At Headingley, wouldn’t you want, like me, to maximize Australia’s chance to be 3-0 and like for them to be compensated additional runs in case they are put into bat first under unfavorable conditions or made to bat last in a foreseeably deteriorating pitch.

Best

Thank you Bunratty for your kind comments.

Thanks Les. I have an axiomatic preference for a contest to be settled largely by skill rather than by luck. Thats why I prefer the 100m at the olympics to watching the daily lotto. You may have more of a liking for a greater role for chance in determining outcome. I am glad that despite the axiomatic divergence, we still enjoy the same game of cricket.

Paul, thank you for your critique. To answer the some of your questions I reference the article linked to at the bottom below for reading more than my paraphrasing below.

1. The summary from the article linked to states “The data suggest that winning the toss increases the chance of winning by a small (∼ 2.8\%) but significant margin.”. So the advantages translate to changes in win probability.

2. The above answers your second question to some extent. The study also notes “advantage varies heftily and systematically, by playing conditions” … “winning the toss in conditions where the toss grants a greater advantage, for e.g., in day and night matches, has a larger impact on the probability of winning”. So yes, the advantage seems to matter.

3. In a 100m dash, and for that matter most of track and field, all competitors start from the same line. In basket ball, teams alternate sides every quarter. So sport makes an eliminate to control variables that could affect outcome to the extent it can. The advantages conferred by the existing toss can be mitigated through mechanisms such as what I describe. You are right that this will not eliminate every source of randomness or favorability and you may also be right that my original statement may have been too strong. However, the argument “make equitable whats possible” is a stronger argument than “we cannot have complete equity so lets ignore whats possible”.

4. Captains routinely complain that the toss affected the outcome or at least indicate that the toss mattered to the result. (I cant systematically augment this but I hope you agree.) Even if captains haven’t called for a change, studies have shown how win probabilities are affected by the toss. Fans, are as big, if not bigger, stakeholders of the game. The next world cup is in India, where the final will likely be a day-night match and furthermore dew factor matters for win probability. I quote from the study below “In one-day matches, the advantage of winning the toss in a day and night match is 5.92%,” I am hoping, you, like me, will not want to see this win probability advantage conferred to the side that wins the toss in the world cup final. It seems to me, therefore, that something is broken.

Also please see link below.

https://arxiv.org/abs/1605.08753

Thanks Gavan. I agree with you that complexity should not be needlessly introduced. However, consider the following.

1. How would you deal with toss related advantages for elimination games in the world cup or in situations where each teams meets just once such as in the world cup league stages?

2. Even for test series, your proposal may only even out in the long run. The first test may have very significant favorable conditions, such as rain, that can be acted upon by judiciously choosing whether to bat first or to field first. The second test may not have the same material advantage for the toss (another e.g. first is a day night test and second isn’t). So alternating coin toss wins may not adequately address the issue. The additional complexity introduced in the proposal attempts to provide a fair outcome for each individual contest.

Thank you Marcus. I debated your suggestion myself before settling in favor of the fifth hypothetical as above. There are two considerations to my reasoning.

( A ) The fair value of two independent evaluations is likely to be closer to the average of the two evaluations than either of one of the evaluations is . This is why for e.g. the poll of polls, which averages across polls, is closer to the truth than any one poll. In that sense, the average of two teams evaluations for whats fair is probably closer to the real fair assessment of the value of the conditions. Put differently, two heads are better than one head (and a tail 🙂 )

( B ) Consider a situation where team A bids 31 runs to bat first and team B bids 1 run to field first. Settling at 0, and allowing A to bat first makes the settlement hugely in favor of A. The proposal is to have A bat first and award to B 15 runs ({31 – 1}/2). This seems fairer.

Thank you Presto. Your view is similar to that of other friends of mine.

If you believe traditions of the gentleman’s game must be left alone independent of whether it is good for the game or not, then theres no good argument to make any change to the game. Such a stance will obviate the inclusion of DRS, neutral umpiring, and the changes introduced to the traditions following Jardines introduction of leg theory.

However, if you believe the tradition of the game includes a tradition of making changes towards fairness then there’s potentially a debate to be had on what makes things fairer. Right now, the coin toss confers a statistically significant advantage to the team that calls correctly.

Thank you Marcus for your input. I understand where your coming from and debated this myself before settling on the motivation for the fifth hypothetical as below.

(A) The real fair value of a pitch is likely to be closer to the average of two independent fair evaluations than to either evaluation. (It’s similar to an average of polls is likely to be closer to the truth than any one poll). By settling at the average we retain the above property. Put differently two heads are better than one head (and one tail. ????)

(B) Consider a situation where team A wants to bat first and bids 19 runs. Team B wants to field first and bids 1 run. If we settle at 0 and let both teams get they want, it’s very much settled hugely in favor of A. The proposal is to settle at (19-1)/2 or 9 runs for B who will field first.

Thanks.